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Hürlimann, W (2014)

A first digit theorem for powers of perfect powers

Communications in Mathematics and Applications 5(3), pp. 91-99.

ISSN/ISBN: 0975-8607 DOI: Not available at this time.

Abstract: For any fixed power exponent, it is shown that the first digits of powers from perfect power numbers follow a generalized Benford law (GBL) with size-dependent exponent that converges asymptotically to a GBL with half of the inverse power exponent. In particular, asymptotically as the power goes to infinity these first digit sequences obey Benford's law. Moreover, we show the existence of a one-parametric size-dependent exponent function that converge to these GBL's and determine an optimal value that minimizes its deviation to two minimum estimators of the size-dependent exponent over the finite range of powers from perfect power numbers less than $10^{5m \cdot s}$, $m = 2,\ldots,6$, where $s = 1,2,3,4,5$ is a fixed power exponent.

@article {, AUTHOR = {Werner H{\"u}rlimann}, TITLE = {A first digit theorem for powers of perfect powers}, JOURNAL = {Communications in Mathematics and Applications}, YEAR = {2014}, VOLUME = {5}, NUMBER = {3}, PAGES = {91--99}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Number Theory